Ethical Data Science
Protected Characteristics under the Equality Act (2010)
Mapping from human to mathematical concept, many measures of fairness.
Binary outcome \(Y \in \{0,1\}\).
Binary Prediction \(\hat Y \in \{0,1\}\).
Protected attribute \(A\) takes values in \(\mathcal{A} = \{a_1, \ldots, a_k\}\).
The probability of predicting a ‘positive’ outcome is the same for all groups.
\[\mathbb{P}(\hat Y = 1 | A = a_i) = \mathbb{P}( \hat Y = 1 | A = a_j), \ \text{ for all }\ i,j \in \mathcal{A}.\]
Among those who have a true ‘positive’ outcome, the probability of predicting a ‘positive’ outcome is the same for all groups.
\[\mathbb{P}(\hat Y = 1 | A = a_i, Y =1) = \mathbb{P}( \hat Y = 1 | A = a_j, Y=1), \ \text{ for all }\ i,j \in \mathcal{A}.\]
Among those who have a true ‘positive’ outcome, the probability of predicting a ‘positive’ outcome is the same for all groups.
AND
Among those who have a true ‘negative’ outcome, the probability of predicting a ‘negative’ outcome is the same for all groups.
\[\mathbb{P}(\hat Y = y | A = a_i, Y =y) = \mathbb{P}( \hat Y = y | A = a_j, Y=y), \ \text{ for all } \ y \in \{0,1\} \ \text{ and } \ i,j \in \mathcal{A}.\]
The probability of a true ‘positive’ outcome for people who were predicted a ‘positive’ outcome is equal across groups.
\[\mathbb{P}(Y = 1 | \hat Y = 1, A = a_i) = \mathbb{P}(Y_1 = 1 | \hat Y = 1, A = a_j) \ \text{ for all } \ i,j \in \mathcal{A}.\]
Even in this simple case there are so many ways you can consider fairness.
Some metrics rely on knowing the true outcome.
Sampling issues: inference or tolerance bounds.
Conditional probability is hard.
\(L = w_1 * \text{fit} + w_2 * \text{fairness}\)
Minority Groups: Re-weight in loss function or up-sample.
Historical Bias: Forgetting factor to down-weight older observations.
Feedback loops: need direct intervention.
Meta-modelling one way of doing this.
Effective Data Science: Ethics - Fairness - Zak Varty